We seek a method by which the residual strengths of composites subjected to combined degradation mechanisms may be calculated. Three different approaches are considered. First, the inputs to the residual strength analysis are purely phenomenological. Second, we make use of a micromechanics-based simulation to combine the effects of two specified damage mechanisms. Finally, we develop a hybrid approach in which the results from the micromechanics simulations for individual mechanisms are used as inputs to the residual strength model as if they had been obtained from experimental data. The residual strength model is then used to predict the combined behavior, and the results are compared with those obtained directly from the simulations. For the two mechanisms considered (slow crack growth and asperity creep), the results for the detailed micromechanical simulations were accurately represented by the residual strength-based model.